Step 1

Position a rack in the middle of the oven and preheat to 375 degrees.

Step 2

If using fresh peaches, bring a 4-quart pot of water to a boil over high heat, and have ready a large bowl filled with ice water nearby. Using a paring knife, score the skin of each peach from end to end, but leave the peach intact. Place the peaches in the boiling water for 30 seconds. Then, using a slotted spoon, transfer the peaches to the ice water for 30 seconds. Use the paring knife to remove the skin from the peaches, then halve and pit the peaches, and quarter each peach half.

Step 3

In an 8-inch square baking dish, toss together the peach wedges, cherries, 2 tablespoons of the honey, the lemon zest and juice, and the cornstarch until well combined.

Step 4

To make the topping, in a food processor, combine the flour, baking powder, baking soda and salt and pulse a few times to blend. Add the butter and pulse until pebble-size pieces form, about 10 pulses.

Step 5

In a small bowl or pitcher, whisk together the buttermilk, oil and the remaining 1 tablespoon of honey. Add to the food processor, then pulse again just until the mixture is moistened. Drop the batter in six mounds on top of the fruit and sprinkle with the demerara sugar, if using.

Step 6

Bake for 30 to 40 minutes, or until the fruit is bubbling and the biscuits are cooked through and golden brown. Let rest 5 minutes before serving.